Puzzles, situation puzzles and recreational mathematics.

Neuron juice.

3.14159... NUMBER PI. NEURON JUICE.

The story of pi reflects the most seminal, the most serious, and sometimes the most whimsical aspects of mathematics. A surprising amount of the most important mathematics and a significant number of the most important mathematicians have contributed to its unfolding —directly or otherwise.

Pi is one of the few mathematical concepts whose mention evokes a response of recognition and interest in those not concerned professionally with the subject. It has been a part of human culture and the educated imagination for more than twenty-five hundred years.

The computation of pi is virtually the only topic from the most ancient stratum of mathematics that is still of serious interest to modern mathematical research." (From the introduction of "Pi: a Source Book", by L. Berggren, J. Borwein and P. Borwein.)

Definition of pi, by Wikipedia

The number π is a mathematical constant, the ratio of a circle's circumference to its diameter. It is used in mathematics, physics and engineering. The first ten decimals of pi are as follows: 3.1415926535...

And one of the definitions I have appreciated the most (thanks to Mr. Marcelo Juarez)

1) Take a cylindrical can. 2) Take some thread. 3) Cut the thread exactly like the perimeter of the cylinder (a complete turn) 4) Number pi means that the thread measures 3 times the diameter of the cylinder and there is a little bit left, which corresponds to 0.14... of the diameter. That's why it is 3.14... I only got to understand the explanations of the teachers through this kind of examples.

History of number pi

The fist known reference to pi is from approximately 1650 BC in Ahmes's Rhind Mathematical Papyrus. It is a document written in a 6m-long and 33cm-wide piece of papyrus. It contains basic mathematical problems, fractions, area and volume calculation, progressions, proportional distribution, rule of three, linear equations and basic trigonometry. The given value of pi is 28/34 ~ 3.1605.

One of the first approximations was the one given by Archimedes in 250 BC, who calculated its value between 3 10/71 and 3 1/7 (3.1408 y 3.1452) and used in his studies the value 211875/67441 ~ 3.14163.

Leonhard Euler began to use the popular symbol π in 1737 and it became immediately a standard notation.

In the computer age, one of the ways of verifying the effectiveness of a machine was to use it to calculate decimals of pi. In 1949, a ENIAC computer calculated 2037 decimals in 70 hours; in 1966 a IBM 7030 got to calculate 250,000 decimals in 8 hours and 23 minutes; and in the 21st century, in 2004, the supercomputer Hitachi spent 500 hours working to calculate 1.3511 trillion decimals.

How to calculate the value of pi

One of the ways of finding out the value of pi is calculating the perimeter of a polygon with many faces which is inside a circle of known diameter. The more faces has the polygon, the similar to the circumference it will look, and its perimeter will be closer to the length of the circumference.

Numerical value of pi

Being an irrational number, its value can't be calculated in a numerical way accurately, there will always be another decimal after the latest one. Just out of curiosity, here you have the first 1000 decimals of pi.